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If x = dtt∫0ydt1+9t2 and ddd2ydx2 = ay, then a equal to ______. - Mathematics

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Question

If x = `int_0^y "dt"/sqrt(1 + 9"t"^2)` and `("d"^2y)/("d"x^2)` = ay, then a equal to ______.

Options

  • 3

  • 6

  • 9

  • 1

MCQ
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Solution

If x = `int_0^y "dt"/sqrt(1 + 9"t"^2)` and `("d"^2y)/("d"x^2)` = ay, then a equal to 9.

Explanation:

Since x = `int_0^y "dt"/sqrt(1 + 9"t"^2)`

⇒ `"dx"/"dy" = 1/sqrt(1 + 9y^2)`

which gives `("d"^2y)/("dx"^2) = (18y)/(2sqrt(1 + 9y^2)) * "dy"/"dx"`

= 9y.

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Definite Integrals
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Q 25
Chapter 7: Integrals - Solved Examples [Page 161]

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NCERT Exemplar Mathematics [English] Class 12
Chapter 7 Integrals
Solved Examples | Q 25 | Page 161

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